Math Is Fun Forum

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Hello, I think the answer for
http://www.mathopolis.com/questions/q.php?id=589
Have a typo.
Q : 3 years ago you had $120 in the bank. You now have $192.
If the amount of money at the end of each year increases exponentially, then how much will you have in the bank after another 7 years?
(Assume that you do not deposit or withdraw any money)

A : Start with the formula y(t) = aekt
We know y(0) = 120
⇒ 120 = ae0
⇒ a = 120

We also know y(3) = 192
⇒ 192 = 120e3k
⇒ e3k = 192 ÷ 120 = 1.6
⇒ 3k = ln(1.6) = 0.470...
⇒ k =  0.470... ÷ 3 = 0.156668...

Now we know a and k, we can write the growth function y(t) = aekt explicitly as
y(t) = 120e0.156668t

Now, we can find how much money there will be in the bank after a further 6****(isn't this 7) years by replacing t with 10:

y(10) = 120e0.156668 × 10
= 120e1.56668
= 120 × 4.79071658...
= 574.89

You will have $574.89 in the bank after a further 7 years

Sorry if I was wrong, please explain.

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Hi;

My #589 is about rabbits.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Chooipian, your answer is right.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Hi chooipian;

Please learn to use latex.

http://www.codecogs.com/latex/eqneditor.php

And find the correct link to the question that I may edit it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

oops... http://www.mathopolis.com/questions/q.php?id=1238 How to use latex here?

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

It is the second question not the first.

http://www.mathopolis.com/questions/q.php?id=589&site=1&ref=/algebra/exponential-growth.html&qs=589_1238_1239_2304_2305_8089_8090_8091_8092

edit:  If you put the second page link in, you get the first question.  Does that always happen or is there a bug?

and chooipian's answer is correct.  I chose answer C and was told I'm correct with that answer.

Bob

Last edited by Bob (2014-05-29 01:37:42)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Take what codecogs spits out and put it between

Hi Bob;

If you put the second page link in, you get the first question.  Does that always happen or is there a bug?

Looks like a bug.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

hmmm.  id = 1238 leads to question 2 but my screen has question 2 and id = 589.

I've not played with these questions so I've not tested this before.

maybe chooipian got directed to the wrong answer link.

Bob

Last edited by Bob (2014-05-29 01:42:46)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

I am getting C, so what is the problem?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

Now, we can find how much money there will be in the bank after a further 6 years by replacing it with 10:

It should be 7 not 6.

Last edited by David (2014-05-29 02:17:03)

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mathpolis - Question 2 Algebra 2 Hard (Exponential Growth and decay)

I got it! Thanks for spotting it.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.